Why the Moon Points Up After Sunset: A Visual Paradox Explained
Lunar Terminator Paradox
The lunar terminator paradox describes how the illuminated part of the moon can point upward after sunset, even though the sun is below the horizon. By writing a program to simulate the geometry, the author shows that when the moon is high in the sky, we view it from below, revealing a dark slice at the bottom that makes the bright side appear to point up. The effect is strongest for a nearly full moon. The author also notes that AI tools like Claude and Gemini failed to grasp the concept, making circular arguments.
They were both completely unable to comprehend this, and would make infinite circular arguments. Clearly they read some incomplete explanations on the internet (as I have), and lack the reasoning capability necessary to distill it into something resembling "understanding". AGI is not here yet.
- j1mr10rd4n
To me, this article conflates lunar elevation and phase. Together with the use of ambiguous terms "up", "down", "above", and "below" makes it difficult to understand the author's intent and what their software is meant to visualise.
Lunar elevation (aka "altitude" in celestial coordinates) is sidereal, so the maximum range is determined by the viewer's latitude. The moon's orbital plane is not perfectly aligned with that of the sun-earth so there's another component there, but this only varies +/- 5 degrees of the sun's declination.
Lunar phase is synodic, so there's no significant variation in the observed illuminated portion with the moon's elevation over one night.
The full moon occurs when the moon is on the opposite side of the earth from the sun, so it rises at sunset, transits the meridian at midnight and sets at sunrise, (+/- a few minutes for seasonal variation).
Here's a nice visualisation of the lunar analemna - the figure described by the apparent position of the moon over a month - from Mt. Laguna at 32.8 degrees north. https://www.hpwren.ucsd.edu/news/20250212/
I also found this page with a decent explanation of the apparent effects of orbital cycles.
- Veedrac
Simple way to imagine this in your head.
Hold two ping pong balls at arms' length, one above and further away than the other. Right now you are the sun.
Put a red dot on top of the lower one, and then rotate it just slightly until you can't see it. This is the observer on Earth, who is after sunset.
Put a red dot directly in the middle of what you can see on the upper ball. This is the center of where the sun is striking the moon.
Keep looking at this dot on the moon. Now, keeping their relative positions fixed, bring the balls towards you and up, until you are looking from the perspective of the observer on Earth. What happens to the dot on the moon? It appears to rise up away from you.
That's the paradox.
- dvh
> Now, what happens if the moon is not at the horizon, but higher up at the sky?
Moon follows the sun to the west so to move moon "higher" up in the sky you need to rewind time (15deg/hour). In e.g. 4 hours moon barely moves in it's 28 day cycle so the moon will look exactly the same (you can take a picture and compare). It's the earth rotation that make moon "go down" or up. I've read your article 2 times and I still don't understand what is apparent problem, no wonder AI had trouble. Also it's hard to reason about up and down when moon move along ecliptic which is curve. Down at noon points elsewhere as down at sunset.
- divbzero
This isn’t really a paradox if you just visualize the Moon as a sphere and visualize where the Sun is shining from, and I think that’s what the plots in OP demonstrate.
The “paradox” might be in the initial assertion which does not use an accurate mental model: “After sunset, the sun is below, so we would expect the illuminated portion of the moon to point down, towards where the sun is.” This assertion might be true if at sunset the Sun ducks just behind the horizon, around the same distance or closer than the Moon is to the Earth. In reality, the Sun is of course much farther from Earth than the Moon. Factoring the relative distances into the mental model will lead you to the correct conclusion.
- Sharlin
The sky is spherical, so straight lines in the sky aren’t straight lines on its 2D projection on the retina. Rather, straight lines are great circles. So if you trace the great circle that connects the sun and the moon, the moon should "point" along that great circle – which can be considerably off of what we think of as a straight line (which is curved in reality).